The first simultaneous images of the auroras in the Northern and Southern Hemispheres with a single camera have been gained with the Earth Camera onboard the Polar spacecraft with sufficient angular resolution to provide maps of the intensities. An auroral substorm was fortuitously observed on 1 November 2001 when the spacecraft was favorably positioned to observe both auroras. The auroral intensities during the onset and the early expansive phase were mapped into corrected geomagnetic coordinates. The onset brightening at far-ultraviolet wavelengths was first detected in the southern auroras and subsequently seen in the northern auroras about 1 min later on L-shells of about 5 RE. During the early phases of the auroral expansive phase, the southern aurora continued to be brighter. The unequal auroral intensities in the two hemispheres suggest that there is strong coupling of the ionosphere and magnetosphere. The mapping of the auroras revealed that there is a local time difference between the onset positions of about 40 min, with the southern auroras positioned to the east relative to those in the north. This displacement was also similarly detected in the quiet auroral regions, which were not participants in the auroral substorm. Such displacements may be useful in developing improvements in the accuracy of global magnetic models that are important for determination of the position of the in situ particle and field measurements in the magnetosphere. The greater brightness of the northern quiet time auroras by tens of percent as first reported by aircraft observations at visible wavelengths in both hemispheres has been verified by the more global view from the Polar spacecraft.